Iterates of $M_1$

Abstract

Assume ${\mathbf{\Delta }}_2^1$-determinacy. Let $L_{{\kappa }_3}[T_2]$ be the admissible closure of the Martin-Solovay tree and let $M_{1,\infty }$ be the direct limit of $M_1$ via countable trees. We show that $L_{{\kappa }_3}[T_2]\cap V_{u_{\omega }}=M_{1,\infty }|u_{\omega }$.

23 pages